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Galactic-Scale Energy

Since the beginning of the Industrial Revolution, we have seen an impressive and sustained growth in the scale of energy consumption by human civilization. Plotting data from the Energy Information Agency on U.S. energy use since 1650 (1635-1945, 1949-2009, including wood, biomass, fossil fuels, hydro, nuclear, etc.) shows a remarkably steady growth trajectory, characterized by an annual growth rate of 2.9% (see figure). It is important to understand the future trajectory of energy growth because governments and organizations everywhere make assumptions based on the expectation that the growth trend will continue as it has for centuries—and a look at the figure suggests that this is a perfectly reasonable assumption. (See this update for nuances.)

Total U.S. Energy consumption in all forms since 1650. The vertical scale is logarithmic, so that an exponential curve resulting from a constant growth rate appears as a straight line. The red line corresponds to an annual growth rate of 2.9%. Data source: EIA.

Growth has become such a mainstay of our existence that we take its continuation as a given. Growth brings many positive benefits, such as cars, television, air travel, and iGadgets. Quality of life improves, health care improves, and, aside from a proliferation of passwords to remember, life tends to become more convenient over time. Growth also brings with it a promise of the future, giving reason to invest in future development in anticipation of a return on the investment. Growth is then the basis for interest rates, loans, and the finance industry.

Because growth has been with us for “countless” generations—meaning that everyone we ever met or our grandparents ever met has experienced it—growth is central to our narrative of who we are and what we do. We therefore have a difficult time imagining a different trajectory.

This post provides a striking example of the impossibility of continued growth at current rates—even within familiar timescales. For a matter of convenience, we lower the energy growth rate from 2.9% to 2.3% per year so that we see a factor of ten increase every 100 years. We start the clock today, with a global rate of energy use of 12 terawatts (meaning that the average world citizen has a 2,000 W share of the total pie). We will begin with semi-practical assessments, and then in stages let our imaginations run wild—even then finding that we hit limits sooner than we might think. I will admit from the start that the assumptions underlying this analysis are deeply flawed. But that becomes the whole point, in the end.

A Race to the Galaxy

I have always been impressed by the fact that as much solar energy reaches Earth in one hour as we consume in a year. What hope such a statement brings! But let’s not get carried away—yet.

Only 70% of the incident sunlight enters the Earth’s energy budget—the rest immediately bounces off of clouds and atmosphere and land without being absorbed. Also, being land creatures, we might consider confining our solar panels to land, occupying 28% of the total globe. Finally, we note that solar photovoltaics and solar thermal plants tend to operate around 15% efficiency. Let’s assume 20% for this calculation. The net effect is about 7,000 TW, about 600 times our current use. Lots of headroom, yes?

When would we run into this limit at a 2.3% growth rate? Recall that we expand by a factor of ten every hundred years, so in 200 years, we operate at 100 times the current level, and we reach 7,000 TW in 275 years. 275 years may seem long on a single human timescale, but it really is not that long for a civilization. And think about the world we have just created: every square meter of land is covered in photovoltaic panels! Where do we grow food?

Now let’s start relaxing constraints. Surely in 275 years we will be smart enough to exceed 20% efficiency for such an important global resource. Let’s laugh in the face of thermodynamic limits and talk of 100% efficiency (yes, we have started the fantasy portion of this journey). This buys us a factor of five, or 70 years. But who needs the oceans? Let’s plaster them with 100% efficient solar panels as well. Another 55 years. In 400 years, we hit the solar wall at the Earth’s surface. This is significant, because biomass, wind, and hydroelectric generation derive from the sun’s radiation, and fossil fuels represent the Earth’s battery charged by solar energy over millions of years. Only nuclear, geothermal, and tidal processes do not come from sunlight—the latter two of which are inconsequential for this analysis, at a few terawatts apiece.

But the chief limitation in the preceding analysis is Earth’s surface area—pleasant as it is. We only gain 16 years by collecting the extra 30% of energy immediately bouncing away, so the great expense of placing an Earth-encircling photovoltaic array in space is surely not worth the effort. But why confine ourselves to the Earth, once in space? Let’s think big: surround the sun with solar panels. And while we’re at it, let’s again make them 100% efficient. Never-mind the fact that a 4 mm-thick structure surrounding the sun at the distance of Earth’s orbit would require one Earth’s worth of materials—and specialized materials at that. Doing so allows us to continue 2.3% annual energy growth for 1350 years from the present time.

At this point you may realize that our sun is not the only star in the galaxy. The Milky Way galaxy hosts about 100 billion stars. Lots of energy just spewing into space, there for the taking. Recall that each factor of ten takes us 100 years down the road. One-hundred billion is eleven factors of ten, so 1100 additional years. Thus in about 2500 years from now, we would be using a large galaxy’s worth of energy. We know in some detail what humans were doing 2500 years ago. I think I can safely say that I know what we won’t be doing 2500 years hence.

Global power demand under sustained 2.3% growth on a logarithmic plot. In 275, 345, and 400 years, we demand all the sunlight hitting land and then the earth as a whole, assuming 20%, 100%, and 100% conversion efficiencies, respectively. In 1350 years, we use as much power as the sun generates. In 2450 years, we use as much as all hundred-billion stars in the Milky Way galaxy. Vertical notes provide historical perspective on how distant these benchmarks are in the context of civilization.

Why Single Out Solar?

Some readers may be bothered by the foregoing focus on solar/stellar energy. If we’re dreaming big, let’s forget the wimpy solar energy constraints and adopt fusion. The abundance of deuterium in ordinary water would allow us to have a seemingly inexhaustible source of energy right here on Earth. We won’t go into a detailed analysis of this path, because we don’t have to. The merciless growth illustrated above means that in 1400 years from now, any source of energy we harness would have to outshine the sun.

Let me restate that important point. No matter what the technology, a sustained 2.3% energy growth rate would require us to produce as much energy as the entire sun within 1400 years. A word of warning: that power plant is going to run a little warm. Thermodynamics require that if we generated sun-comparable power on Earth, the surface of the Earth—being smaller than that of the sun—would have to be hotter than the surface of the sun!

Thermodynamic Limits

We can explore more exactly the thermodynamic limits to the problem. Earth absorbs abundant energy from the sun—far in excess of our current societal enterprise. The Earth gets rid of its energy by radiating into space, mostly at infrared wavelengths. No other paths are available for heat disposal. The absorption and emission are in near-perfect balance, in fact. If they were not, Earth would slowly heat up or cool down. Indeed, we have diminished the ability of infrared radiation to escape, leading to global warming. Even so, we are still in balance to within less than the 1% level. Because radiated power scales as the fourth power of temperature (when expressed in absolute terms, like Kelvin), we can compute the equilibrium temperature of Earth’s surface given additional loading from societal enterprise.

Earth surface temperature given steady 2.3% energy growth, assuming some source other than sunlight is employed to provide our energy needs and that its use transpires on the surface of the planet. Even a dream source like fusion makes for unbearable conditions in a few hundred years if growth continues. Note that the vertical scale is logarithmic.

The result is shown above. From before, we know that if we confine ourselves to the Earth’s surface, we exhaust solar potential in 400 years. In order to continue energy growth beyond this time, we would need to abandon renewables—virtually all of which derive from the sun—for nuclear fission/fusion. But the thermodynamic analysis says we’re toasted anyway.

Stop the Madness!

The purpose of this exploration is to point out the absurdity that results from the assumption that we can continue growing our use of energy—even if doing so more modestly than the last 350 years have seen. This analysis is an easy target for criticism, given the tunnel-vision of its premise. I would enjoy shredding it myself. Chiefly, continued energy growth will likely be unnecessary if the human population stabilizes. At least the 2.9% energy growth rate we have experienced should ease off as the world saturates with people. But let’s not overlook the key point: continued growth in energy use becomes physically impossible within conceivable timeframes. The foregoing analysis offers a cute way to demonstrate this point. I have found it to be a compelling argument that snaps people into appreciating the genuine limits to indefinite growth.

Once we appreciate that physical growth must one day cease (or reverse), we can come to realize that all economic growth must similarly end. This last point may be hard to swallow, given our ability to innovate, improve efficiency, etc. But this topic will be put off for another post.

Acknowledgments

I thank Kim Griest for comments and for seeding the idea that in 2500 years, we use up the Milky Way galaxy, and I thank Brian Pierini for useful comments.

76 thoughts on “Galactic-Scale Energy”

Cold fusion, if it ever worked, would be subject to the same restrictions. As long as we want to use the energy to drive, build, light, heat, cool, or whatever, the end result is heat. Perhaps this deserves a post of its own, because it may not be an obvious statement. But the short answer is that any technology: real; future; or imagined that provides a source of energy for our activities will necessarily run into the limits explored in the galactic scale energy post.

Fusion in a lab is possible, and has even been done in a tokamak—albeit well below break-even. And some of our best bombs achieve fusion. So it’s definitely in the “real world” rather than the “science fiction” category. But that’s not to say it’s easy. We have to confine a plasma at 50–100 million Kelvin (the sun gets by with 16 million K because it’s big enough to be patient about the “rare” fusion event you get at those temperatures). Hot plasmas have their own ideas about confinement, and this is a technical challenge that scientists have chewed on (with some progress) for some time.

Oh–and the astrophysicist in me can’t help but point out that the sun is about 300,000 times the mass of the Earth—not that it’s a key part of your point.

actually I believe the JET reactor in england has acheived break even (Q=1) and the ITER reactor being built in France will achieve Q=20.
*disclaimer: Q is defined as energy output of all the fusion events divided by the energy required to heat the plasma

This is brilliant! Thanks! I’ll have to pass it along to my friends and kids (with lots of explanation).

It’s too bad we use the same word – law – for human “laws” and physical laws. I suspect a lot of people would read this and think “Thermo-something limits? Tosh! That’s just some environmental wacko talking.” To which we would say, “No, no. Those are the laws of thermodynamics – it’s physics, not environmentalism.” Then they’d respond, “‘Laws’ of thermo-whatever?!? I bet the Democrats passed those laws. We’ll just change them!”

Heh. I’ve dealt with folks who instead give a bit more seemingly “smarter” answer. But the answer is fundamentally flawed and is grounded in the narrative of our society, that so-called Technology and Human Genius has provided us everything and thus it can also _bend_ , _push_ and _break_ natural laws (people cite stuff such as “Moore’s law” as though those were real natural ‘laws’)… At which point I give up and figure out a better use of my time. Sometimes, they also cite examples of how some ‘theories’ were proven wrong later and hence it is likely that even the Laws of Thermodynamics _might_ be changed in the future… at which point, I categorize them as the people who are in Denial[*] and I move on with life.

It seems like a better term for “natural law” would be something like “effect.” I realize that it’s normally used to refer to something less coherent than a law, but it seems to capture the meaning more effectively… 🙂

On the topic of thermodynamic innumeracy, remember the end of Spiderman 2, when they quench a runaway fusion reaction by throwing it into the east river? Sigh.

This is curious because it comes from a university website where there surely is an economics department. I wonder how many of the 57 (assuming I counted correctly) faculty members in economics at UCSD acknowledge that there are hard physical limits to economic growth.

Is the answer greater than zero? I suspect not. Are economics faculty immune to math and physics?

They are not immune. They just do not yet find it relevant. When things like debt ceilings are being reached in a matter of days, events such as those outlined here are simply too far away to consider…yet. No I am not an economist, but I have asked a number of them about this and that appears to be their fairly uniform answer.

Of course, the economists are right too. Since money is not founded in anything fundamental – it is *technically* possible to keep Growing money. Since GDP is measured ultimately by how much ‘value’ (money) was created, they believe they can achieve most of that ‘growth’ in areas such as mobile advertising and social networks. What awesomeness! This is the case of sticking one’s heads up in the Cloud (of the Amazon kind).

Even the growth of money has an upper bound, to do with the information density which can be achieved using space and matter, and the restrictions on the speed at which signals can propagate. For money to mean anything at all the two states GDP = x and GDP = x+1 must be in-principle distinguishable, which demands around log_2 (x) bits of information storage to write x down somewhere. There is a maximum number which is humanly attainable using the reserves of matter and energy in our grasp.

The thermodynamic constraints described in the main article would ruin us far before we encounter this counting limit, but it is still there. There is no scope in any world with bounded maximum signal propagation speed for exponential growth of anything measurable.

The second law is a fraud! Yes, that’s right, I said it, and have liberated every scientist in the field of bio-activity, excluding those of the micro-bio-mechanics who use reductionary procedures out of sheer laziness. Life develops, perpetually, and ironically during periods of mass extinction we find the greatest levels of systemic shift in energy consumed, bio-migration of material, and further potential for future upshifts. If only physicists realized they were alive, and those mundane accountants we today call economics would stop relying on the dead science of physics.

“Your little asteroid has a six-billionth of the earth’s total surface area. It is a sphere with a radius of 82 meters, and with a surface area of about 85,000 square meters. That, depending on how you prefer to think about it, is almost exactly 21 acres, or 8.5 hectares. In more urban terms, that is 19 American football fields, or about 12 English football (professional soccer) fields.

Just over 70 percent of your 21 acres is covered by salt water. If it were to freeze over, you could walk from any point to any other point at a leisurely pace in under ten minutes. Since the ocean covers fifteen acres, the land surface covers the remaining six acres.”

This piece is really an excellent demonstration of the absurdity of indefinite growth. It’s really great to go beyond simply “infinite growth on finite planet” adage, which though obvious to people who already agree, maybe too abstract a statement. It’s really a great read, thanks!

Unfortunately, I believe it is too late to convince a enough people fast enough that we have to stop endless growth. There’s simply too much “invested” in indefinite growth.

… But people continuing to believe in more growth doesn’t actually mean they’ll get what they wish. At some point, as this article demonstrates, further growth is simply not feasible and will stop or reverse. It’s at this moment I think (one of) the tasks of the environmental movement is to prepare for.

In particular, the energy technology we decide to fall back on I think will be determinant in humanity’s well fare. For instance, falling back on dirty fossil or bio-carbon may simply destroy the planet outright (regardless of energy savings: if Europe maxed out on biological capacity in the high-renaissance, what chance do we have now of relying on biological energy sustainably with more people, more expectations, and less local renaissance craftsmen).

Sunlight, though can’t save growth, has some interesting characteristics. First, it’s a thermal energy source and the most energy we use (and actually need to survive) is thermal energy. Second, sunlight is the “primary ecological energy source” so that using sunlight directly doesn’t destroy the result of a long ecological process (the real efficiency of biological energy sources must be measured against the sunlight required to create that bio-energy, not simply how well we are then able to burn it). Third, direct solar energy can be used locally reducing the need for transportation and huge infrastructure. So direct solar technology is one advantage that could have over the pre-industrial age that (at least in Europe) was already unsustainable.

Great Read. By the way, in 1972 the Club of Rome published a report called “The Limits to Growth”. Interestingly, beginning from the 1980s (almost) nobody cares about their predictions. Very sad indeed.

A veritable classic! The follow ups (1992 “More limits to Growth”, and “Beyond the Limits” were the titles, I think), only served to prove that the working models originally used were remarkably accurate.

Good post. I think you could have added another sentence on the thermodynamics in layman’s terms – i.e. that a certain percentage of the generated energy will invariably end up as heat (thermal energy). Btw, what was that percentage for your calculation? And yes, as a physicist, I find it mind-blowing how this fixation on continuous growth can still be perpetuated. In fact, I personally find we have already taken it too far. The typical example is the life span of commodities. Whilst they could be produced to last a VERY long time, they are usually engineered to last just beyond their warranty period – that design harvests maximum profit in the long run. I mean, really, for most of us, our first or second mobile phone would still do perfectly. But what happens is that every 2 years on average, we get a new one. So really, “sustainable” would mean products lasting 4-5 times longer on average, which, inevitably, would also cost (a lot) more than they do now (as the total volume of goods would be significantly smaller).
Anyway, what I think is that curbing output (by higher prices for longer-lasting products) could also have its bright sides – a slower pace of life, which would be more pleasant.

Good point about the thermodynamics. I used 100% in the calculation. Because for any of the activities in which we engage (short of sending light directly into space—which, incidentally, is what I do for a living—virtually all the energy does end up as heat once we’re done. Cars stir the air and this energy ends up dissipating in the viscous regime of small eddies; manufacture and other “useful” work results in heat (the nail is hot after pounding into wood). The only other exception I can think of is the potential energy invested in erecting buildings and mining ores/oil out of deep mines/deposits. But this must be a very minor fraction of the energy budget (and is released as heat when buildings are demolished, for instance).

I looked at this about 1972. I really ticked off the lecturer because he was playing absolutes and it is always easy to point out failure points in arguments like that and all the “believers” can do is get angry.. You are less absolute I suspect, but some of your readers take it as absolute.

So here is a 1972 exception:Hey, if you got 100% efficiency, just use all the energy to create order. No heat until the order goes to disorder, which might take an eternity if we are clever.

For the lay reader, ordering things takes energy and instead of heat, you get order. We are very inefficient at creating order, but the writer let us use 100% efficiency. So …

Interested people might look at information theory stuff starting with a guy named Shannon.

Now, going on, thermodynamics, like most popularized science, is remarkable weak. You might find people talking about the heat death of the universe. But experimental verification of any interesting system as obeying thermodynamic laws is pretty much outside the scope of any permitted discussion, and so we can pretty much figure we really do not know anything deeply. With regard to testing the heat death of the universe because of thermodynamics, you have to stand outside the universe and put the universe in a box. I am not talking practical issues here–the idea simply may not have any meaning. And while we could put earth in a box, the math only really works after you let the planet go into equilibrium. But last I looked the planet has not been in equilibrium for for multiple billions of years. So we have deeply nested assumptions and approximations going on. And at a very deep level, the assumption is that you, the whole biosphere, and the universe is a machine running under a rather simple causality model. Oh well.

Thanks for listening to my rant. This is just the 1972 version though. The current version would make you scream. 🙂

“As we saw in the previous post [this one], the U.S. has expanded its use of energy at a typical rate of 2.9% per year since 1650”

As this is mistaken, conclusions drawn from it are not to be trusted. As I’ve noted in a comment to the following post, total US energy consumption increased only 0.4% per person annually 1959-2009, and *declined* 0.4% per person annually 1973-2009. Computing a figure such as 2.9% on the basis of past population growth times per capita consumption and projecting that indefinitely into the future — when we know that population growth trend has already stopped (and in large part reversed) does not seem sound practice.

But let’s consider that “typical rate of 2.9% per year since 1650” description on its face, assuming it is totally accurate as to the past.

If we think about it a minute, just considering general knowledge, not getting fancy in any way, what does it tell us?

From 1650 to 2011 contains three distinct historical-economic periods in the USA:

1) 1650 to circa 1800: Pre-Industrial Revolution subsistence agriculture economy. Energy efficiency doesn’t improve, if it does at all, at an any faster rate than in the Middle Ages. Life expectancy is circa 30 in the most developed areas, 20s elsewhere, not much different than in the Middle Ages (or in the Roman Empire for that matter).

From this we know any growth in energy use is due entirely to the slow growth in population.

2) From 1800 to circa 2000: Industrial Revolution and first half of the Demographic Transition. Income and wealth per capita grow *immensely* (over 50-fold). Life expectancy zooms to 78. Population grows *immensely* (from 5.3 million to 291.4 million — another 55 fold) due to plunging death rates and much longer life expectancy.

Yet for all this immense economic growth per capita multiplied by a 55-fold growth in population still total energy consumption grew no more than the same 2.9%.

From this we know there was a continuing immense increase in efficiency of energy use compared to period (1).

3) From circa 2000 – onward: Post-Industrial Revolution economy, and second half of Demographic Transition with population declining in advanced economies (except the US where it flattens, largely due to immigration.)

The ongoing increase in energy use efficency continues as before — but now the population is flat (in most developed economies falling).

What’s the most likely course of the trend line of energy consumption going forward from here? The same as in (2) forward indefinitely, or downward?

Let’s also be clear that my plot and analysis is for total energy growth, not per capita. And I think there is some confusion about the nature of 2.9% growth. For instance, in period 2 above, population in the U.S. increased 55-fold in 200 years. This corresponds to 2.0% annual growth (an explosion!). Meanwhile, the 2.9% growth over the same period produces a factor of 300 growth in energy. But don’t take the math’s word for it. Look at the graph: from 1800 to 2000, energy grew by over two orders-of-magnitude (more than a factor of 100). So this is not at all increased efficiency, as the above comment alludes, but a greater energy intensity per person. It makes sense too. In 1800, you might run a few horsepower. Today it’s vastly more.

I agree that a new phase is coming: population will not keep expanding. But this just reinforces the main point that growth will not continue forever. I do not in all seriousness expect energy growth to continue at 2%+ forever. This post shows how absurd that notion is. Continued growth at 2% is not justified. Exactly.

A thermodynamic energy use limit on Earth is an interesting thought! Though thermodynamics doesn’t limit growth off-world in space stations. Long before it gets too hot you build a new one or bigger radiators. A Type II Kardashev civilization will most definitely not be stuck on Earth. So it’s a fun thought experiment, but I doubt a likely scenario or relevant to the discussion about energy growth.

I think it would be interesting to set an upper bound. I’d love to read an analysis on what the MAXIMUM possible energy growth rate is for human civilization, given the limits of the speed of light and the geometry of the galaxy.

And then an analysis based on a more realistic scenario, e.g. the paper Burning the Cosmic Commons: Evolutionary Strategies for Interstellar Colonization by Robin Hanson, but this time counting the energy use and growth rates.

I’d be interested in analysis assuming humans stay on earth, but almost all manufacturing/refining is done in space. Presumably then fabrication would be solar powered though maybe He3 fusion powered, but not adding to our planet’s heat budget.

“Once we appreciate that physical growth must one day cease (or reverse), we can come to realize that all economic growth must similarly end. ”

This inference is not supported, and is not obviously true. Given that the major part of economic growth is in the idea/information space and that the physical component a given amount of economic value is declining its not clear that the growth must stop. So for instance there is economic value in computation and the amount of energy required per computation is rapidly declining. Its true there are limits here.. but they are a long way off and imply some pretty impressive end results before you hit known physical limits.

You should at least be able to state Julian Simon’s (Ultimate Resource II) argument and offer counter if you want to convince people who are on the other side of the argument.

Also its worth pointing out how much wealth would be improved by 350 years of 2.9 percent growth.. that basically makes the equivalent of an average American GNP per capita about a billion dollars a year!

I did like the energy limits part though and the Dyson Sphere solar array 🙂

Have you read/heard “There’s Plenty of Room at the Bottom” by Richard Feynman? In it he gives the order-of-magnitude physical limits on computation as known in the 1960s (though they are still roughly the same today… quantum computing has pushed them down somewhat… a viable quantum computer benefits in some algorithms exponentially, in others quadratically, versus a classical computer).

Because information must be stored, processed and transmitted in a physical medium exponential growth in information would also lead to exponential energy growth. Limits that feel a ‘long way off’ are surprisingly close when talking about exponential growth and even now the speed of serial computation is not growing at the same rate it used to any more (which feels like a good upper bound on the quality of information that can be created per unit time).

An easily foreseen paradigm shift is that we *grow* our buildings, tools, clothing, communication and computation devices biologically. There would then be little if any need for mining and refining ores, or for fueling transportation. We’d be feeding our possessions rather than fueling them. Our energy consumption could plummet based on that alone, and a world with ten or twelve billion inhabitants could enjoy a good life.

“And think about the world we have just created: every square meter of land is covered in photovoltaic panels! Where do we grow food?”

I’m concerned by this comment. Certainly ‘all energy produced’ ‘in all forms’includes food production from agricultural growth (solar power) so it will also be included in the future production of food (presumably in a near 100% efficient way from the power produced from the near 100% efficient solar power). If your past and current estimates of power production does not accurately include power produced from growing food then you are overstating the rate of power growth as we are shifting power from plants (photosynthesis) to power plants by using electricity in place of manual labor.

Similarly, there’s a serious problem in trying to produce enough food to sustain population growth. First, suppose we decide not to continue ramping up food production as population soars. Then a few billions will die.

Now suppose we ramp up food production to allow the earth’s population to double. And then we do it again, allowing another doubling. We can’t keep doubling food production forever! When we finally give up, eight or sixteen or thirty-two times more billions of people will starve. It seems incredibly heartless to to put a stop to ravaging the earth in order to produce greater amounts of food, but trying to sustain a larger population will lead, eventually, to a far greater calamity.
This is a choice we have to make. A choice between two truly horrible alternatives.
– tobias d. robison

Some topics seem almost taboo in this country, Like population control and any limits to excess. The rather hyperbolically named, but still very worthwhile, video “The Most Important Video You Will Ever See” deserves a mention herehttp://www.youtube.com/watch?v=F-QA2rkpBSY

+1 to the above link. I was going to post it here myself if no one else had. Despite a name that sounds like a joke setup (it was apparently named by one of the students of the professor giving the lecture who wanted to make sure as many people as possible saw it) it really is a fantastic numerical and data-driven exploration of the ramifications of exponential growth in a number of important areas.

One major assumption is that our need for energy will always exceed the available energy, but that may level off. Consider the argument for bandwidth—we can never have enough… until you realize that at some point, you’ll (and every human on the planet) be able to stream more data into your brain than you can possibly ever consume… thus, any extra bandwidth from that point is irrelevant. The same may turn out to be right about energy usage. Once you have your army of robots doing everything you’d ever wanna automate, and you’re constantly hovering in your rocket powered ship (moving about earth at incredible speeds), have your own server farm doing whatever you want, etc., what would you use the extra energy on? Sure you can come up with hypothetical scenarios (e.g. I’d ignite Jupiter into another sun, etc.) but on an individual level, there’s definitely a limit at which point any extra energy doesn’t really contribute to your well being or lifestyle.

Computing. At a certain point the most economically viable life forms become those in a computer, not those in the real world (I refer you to Accelerando for a scifi take on this). Eventually every watt of power becomes the ability to sustain in memory and processing another thinking being.

That’s the point of the article — at some point, given land and food constraints e.g., human populations will plateau; and each of us will have our army of robots, so we won’t need more energy per capita — and if that state of the world happens, then a bank would not be incented to lend money for investment, because it seems unlikely that they’ll be able to find a market for their new investment. And thus, because lending would slow e.g., growth would slow, and you have the conclusion of the article.

This is an attempt to invalidate only one of the problems you present. When discussing the solar panels, 100% efficiency, and surface area, we should consider if solar panels can be made transparent, and stacked on top of each other, or receive mirror reflected heat from nearby towers. This would allow growth beyond the actual land surface area by stacking.

At 100% efficiency all light and heat would become electricity. No light would reach the lower panels in a stack… Sure the heat generated from driving your EV can be absorbed again eventually, but the conditions inside the dome would not be livable. Most importantly, you don’t need a stack.

100% efficiency means that 100% of the light hitting the solar panel is absorbed, meaning none can pass through or be reflected. How can a solar panel absorb 100% of the energy of the electromagnetic radiation hitting it yet pass some on down through to the next one? Conservation of energy much?

From Brian Cox’s “Why does E=mc^2?”:
“So ponderous is the conversion of protons into neutrons that, “kilogram for kilogram,” the sun is several thousand times less efficient than the human body at converting mass to energy. One kilogram of the sun generates only 1/5,000 of a watt of power on average, whereas the human body typically generates somewhat more than 1 watt per kilogram.” I think we saw economic growth outperform energy growth in the last 100 years. I predict we’ll see “entropy growth” outperform energy growth in the next 100. We will get more efficient at entropy conversion. But first we’ll need to recognise the unit of measure. I don’t think anyone has their eyes on this ball yet.

Gotta remember that a W = J/s and that 1kg of the sun will produces many more J’s(energy) in its lifetime than the human body will in its lifetime. So I would be careful saying the human body is more ‘efficient’ than the sun.

I understand that you are trying to be dramatic with showing that continued exponential growth is obviously ridiculous. This is a fair point and one that should be made. My only problem is that you are missing some interesting things in the data that you present.
The fit in the first figure is appallingly bad, especially as you are trying to extrapolate from the data. In the last 50 years energy use has clearly not grown at 2.9%. The exponential fit that you use seems to have an R Squared value of around 0.87, not bad for biology or economics but a physicist should not be impressed. If instead of the exponential fit we try for a logistic function we see a dramatically improved fit, with an R Squared around 0.99.
Logistic functions are useful in modelling situations where we see a natural limit on growth, such as ecological models of animal populations. One of the parameters in the logistic function is the carrying capacity for the system. When I fitted the energy data to a logistic equation the carrying capacity was around 1.4 \times 10^8 billion BTU. The EIA data has 2009 at approximately 0.9 \times 10^8 billion BTU. As is evident in the data the US is no longer undergoing an exponential growth in energy usage instead it has already begun the process of levelling off due to natural constraints.
Exponential growth is not only not a justified assumption to make for the future, it is also not a very good model for what has happened in the recent past.

Thanks so much for this contribution. I’m a big fan of the logistic curve, and could not help but notice the data peeling over. My natural instinct is to say: “aha! rolling over due to natural limits!” But you guess right in that this post is aimed at the person who would not buy that argument, and discounts recent behavior as some oddball anomaly. So I played the fantasy game to show why it deserves to be called a fantasy.

[Edit: see the update post that explores how well the logistic function fits.]

Would also be worried about the impact of the third world steaming ahead with unhindered growth into a Western style economy. Not that I am against people bettering their lives but we must learn from our industrialised mistakes. Concentrate on survival, not becoming rich.

So, this is a great argument for solar energy. Solar energy would already be included in the Earth’s heat load. Storing it and releasing it later would create no net additional heat. And, recycled energy from any sources would add nothing. For instance energy captured during auto braking adds nothing when reused. Don’t create heat, recycle it!

One thing you’re omitting in your analysis is that if we have an energy source which gives us arbitrarily large amounts of power, we can afford to spend the power necessary to keep the planet cool while transferring excess thermal energy to some other planet (the same way an air conditioner works, except on a vastly larger scale). If you don’t mind diminishing returns on increased energy production, you can feel free to use as much as you want. Then too if you don’t mind building a Dyson sphere (even if you supplement it with fusion) you won’t hit the same thermal limit for quite a while longer, as the surface area available for radiation is much higher. A big limit though will be the matter available for fusion, as well as the time it takes to get to other stars.

This excellent analysis couples population with energy consumption, and presumes a 2.3% growth in population. But have you thought about the implications of that assumption alone? The surface of the Earth would have to be densely populated with Republicans (who seem to be 50%, nearly, of the population) and the resulting conflagration would surely destroy the poor planet as we know it.
However the resulting reality distortion field would allow the richest 1% to safely utilize the entire power output of the sun. There would not be sufficient energy for Social Security, though.

Of course if population ceases to grow (as it must), we likely reach flat energy sooner. And then the point is that energy growth has stopped (much sooner than the absurd thermodynamic limits in the post). Not long after, economic growth will likely stagnate as a result.

If commonly accepted theories about the expansion of the universe are true, well then yes, growth, whether of the human or the Borg kind must some day end. But, since we’re up to sci-fi-ish musings anyway, why can’t we as a species grow at a fair fraction of the rate of expansion of the universe itself? That would buy as a few billion years, wouldn’t it, at least until the Big Crunch or Big Chill?

Very interesting article, Tom. As you briefly mention at the end, much of the growth in energy use in the last 400 years has resulted directly from the rapid increase in world population. For example, although US energy usage has increased by 50x in the last ~150 years, energy use per capita has grown much more modestly, by roughly a factor of four (this, interestingly, is the *same* factor by which current per-capita US energy usage outweighs the global average — the world’s residents consume energy on average at the rate we did *before the Civil War*). One could argue, however, that with increasing efficiency of transportation, personal and business electronics, home and office conditioning, etc., energy use per capita is likely to plateau at this level, perhaps even drop slightly in the developed world. At that point, energy growth becomes tied directly to population growth.

I don’t want to trivialize this. This is still a *remarkable* personal allotment of power: each of us in this country consumes on average ~10 kW of power, all day, every day. This is like two giant air conditioners running full blast. It’s also sobering to compare this number to the power we take internally by food and produce directly with our bodies as work (lifting heavy things, for example). This “internal” power supply is roughly 100W. That is, we consume 100x as much energy outside of our bodies as internally (unlike any other animal).

But population growth has *not* remained constant. After peaking at ~2.2% in 1960, it has declined continuously to ~1.1% today, and is projected to continue its decline. If the world’s population peaks at roughly 10B in 2100, and at that point worldwide energy use per capita approaches current US levels, we are dealing with, at peak, a factor of 7 increase in total energy use. This in itself is already a major problem for the climate and our remaining fossil energy reserves, but extrapolating past this point is probably not realistic. Most population growth during this century will happen in parts of the world which consume 5-10x less energy per capita as we do. In fact, fertility and replacement rates drop inversely with per-capita energy use.

So, while I agree with you that the common and unfortunately treasured notion of ever-expanding economic and energetic prosperity is woefully misguided, I think we can actually forecast with reasonable precision (factors of a few) the flattening (but still rather unsustainable) worldwide energy use over the coming century.

Exactly. Thanks for this. Don’t mistake my trip into the absurd as a prediction: it’s more of a cautionary tale for those who have not accepted that growth will stop. Your logical scheme would have energy growth stopping a century from now. I would argue that economic growth in general will stop not long after. Of course supporting 7x our current energy rate may not be in the cards, given the inevitable decline of fossil fuels this century. So the timescale may be much shorter.

snip from above link:
On one level, the fallacy of the “First and Second Laws of Thermodynamics” is simply this: These laws have never been demonstrated to be properties of the real Universe, but only properties of certain closed mathematical-deductive systems, which ignorant or malicious physicists claim to represent the real Universe, but which manifestly do not. On this level, the fraud is identical to that of so-called economists who claim to be able to deduce theorems about the real economy, from supposed self-evident properties of “money.” In fact, the elementary error revealed in the very title of Newton’s famous Principia mathematica philosophiae naturalis (Mathematical Principles of Natural Philosophy) finds itself reproduced, countless times, in textbooks dealing with non-existent “Financial Principles of Economics.”

Contrary to popular academic belief, there are no actual experiments establishing the validity of the “First and Second Laws of Thermodynamics” as universal physical principles. To the extent those “laws” have a certain empirical correlate at all, they are both circumscribed by a purely negative principle, already identified by Leibniz long before the Kelvin-Helmholtz gang came along: the impossibility of a so-called “perpetuum mobile” or “perpetual motion machine”—a hypothetical subsystem of the Universe, able to generate a net surplus of power in the course of a closed cycle, in which the system is supposed to return to exactly its original state, without any other net change in the surrounding Universe.Just as in the case of so-called “impossible” or “imaginary” numbers, the source of the supposed “impossibility” involved is not a limitation of the real physical universe. The limitation is located rather in the notion of a “machine,” as a system describable by the “utopian” Euler-Lagrange form of analytical mechanics. To put it another way: To the extent a physical system is either chosen or forced to mimic the characteristics of a “machine” in the indicated sense, it will appear to obey the First and Second Laws of Thermodynamics. But the Universe as a whole is not a machine; the Universe not only never returns to an earlier state, but its successive states are strictly incomparable with each other from a formal-mathematical standpoint. Thus, the extrapolation of the so-called “First and Second Laws” to the Universe as a whole constitutes the crudest, most elementary sort of scientific error.

If “Universe” refers to the most generalized form of Man’s action upon Nature—no other Universe could be known to us!—then the “state of the Universe” changes fundamentally with each discovery, by some human mind, of a new universal physical principle (power). A formal-mathematical system which (to a first, “engineering” approximation) may have more or less adequately described Man’s physical-economic activity up to that point, now breaks down, as technologies based upon the new principle transform the physical economy to the effect of increasing the relative potential population-density of the human species beyond any a priori “limits.”

The very fact of the successful increase in human population potential by some three orders of magnitude over documented history and prehistory, attests to the existence of a self-developing “power,” lying entirely outside the domain of visible or visible-like objects, but commanding the visible Universe to an increasing extent.

You don’t know what a “law” is in physics then. Many of them are approximations with known exceptions, for example Boyle’s Law, or Charle’s Law or Ohm’s Law. Others, like the laws of thermodynamics, are laws simply because they have no *known* exceptions. It is possible that Dark Energy renders void, or modifies, the laws of thermodynamics.

Why did you choose 1650, over 300 years before the industrial revolution, as starting point for your initial assumption of 2.9% growth? Isn’t that a little arbitrary? Why not start at the end of the last ice age? Or at the emergence of human beings? I’m pretty sure your assumption would not hold.

On the other hand if one only considers the last 30 years, the trend seems to differ from your assumption as well. I can only guess but to me it doesn’t even seem exponential.

Since we don’t have infinite resources to build power plants and infrastructure that might be the limiting factor as it seems to me. Long before any relevant thermodynamic impact effects the earth.

It’s what the EIA has. I was startled to see how consistent the trend was back to before the industrial revolution, so felt it should be shown in its entirety. I make no claim that it would look this way arbitrarily far back: just that this is the regime we’ve seen ourselves in for centuries. And yes, recent times roll over. The post is aimed at those who think we can grow energy forever. The astute will see in the data that perhaps this phase is already petering out.

Good, so 400 years until we reach Type I civilization status, 1300 years until we reach Type II civilization status and 2500 years until we reach Type III civilization status. This is where we should be heading for, if you expect humanity to survive. Wielding the total energy output of the galaxy is not absurd, it’s where we as a species should aspire to go. What is absurd is to expect exponential growth of population, if population grow exponentially, there’s no going to be enough planets to contain all of them.

Based on human nature, its not a choice anybody will make. We will all selfishly strive to improve our lot and as our resources begin to run out, we will move to endless war to get what is left, or at least deprive others of it. We’ll head back to the stone age long before we pop out of existence and the next organisms get their turn on the stage. Between now and then, I’m sure there will be some amazing advances that will let us keep going just a bit longer in relative prosperity.

In business, we see huge growth curves that flatten out as industries mature. Think about “Internet Use” or “Miles Driven by Automobiles Worldwide”. I believe “energy consumption” would most likely fit this sort of scenario.

Hello, while I agree that physical limits to growth are important to discuss and understand (and that economists and humanists do not discuss or understand them), I’d rather assume that if we were using much more energy, it will happen as we go to space.

If we’re using solar system scale energies, it’s possible that practically all economic activity is happening in space, and a significant portion of humans are not living on Earth anymore either.

Space is no magic cure for physical and economical problems. But your assumption that we have to live on Earth while other huge advances in technology happen is not well supported.

It would be interesting to fire some emails if you are going to write about space economic activities and / or space colonization. These are areas where I have some thoughts (they are also areas which contain lots of physically unhinged dreams).

This won’t be the most popular post. While it is always fun to indulge these Malthusian panics there is plenty of evidence even now to show that it will not turn out as forecast here.
Foremost among these is the march to declining growth, followed probably by actual decline, in population. Over a 40 year horizon it will edge up, over a 100 year horizon it will only move up if truly radical increases in lifespan are reached.
Our focus on increasing efficiency in power use has far to go but is clearly started now. An extended use of geothermal energy might even cool the planet slightly to the extent the energy is turned into “stuff”.